Study of shell structure and order-to-chaos transition in warm rotating nuclei with the radioactive beams of SPES

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1 Study of shell structure and order-to-chaos transition in warm rotating nuclei with the radioactive beams of SPES G.Benzoni, S.Leoni, A.Bracco, N.Blasi, F.Camera, F.C.L.Crespi, B.Million,O. Wieland, P.F. Bortignon, G. Colò, E. Vigezzi Università degli Studi and INFN sez. Milano D. Bazzacco, S. Lenzi, S.Lunardi, D.Montanari, C.Ur, et al. INFN Padova and Università degli Studi di Padova G. DeAngelis, D. Napoli, J.J. Valiente-Dobon, et al. Laboratori Nazionali di Legnaro INFN A. Maj, P. Bednarczyk, B. Fornal, M. Kmiecik, M. Ciemala et al., The Niewodniczanski Institute of Nuclear Physics, Polish Academy of Sciences, Krakow, Poland

2 Warm rotating nuclei

3 Collective rotations: de-excitation spectra 168 Yb Analysis of quasi-continuum γ-γ coincidence spectra with statistical and spectral shape analysis methods Fluctuation Analysis Method N µ µ 1 eve N path = 2 1 P E γ2 4 2 /I 4 2 /I E γ

4 ( MeV ) 8E* Realistic Simulation of γ-decay flow: E1/E2 competition Band-mixing Calculations => decay flow simulation 15 n p B n H( I) H def ωj x + V SDI residual J 2I 2 z rot E2 E1 Γ rot extrapolated ρ and Γ rot n b = S if f 2 onset of damping n b = Yb ε = 0.25 I = levels U 2.5 MeV 2 0 Γ rot I-2 I I+2 20 I (h) 60 microscopic discrete levels yrast A. Bracco et al. PRL76(1996) 4484

5 Main Results from the Analysis of Quasi-Continuum Rotational Spectra Evidence for rotational damping Ö Sensitivity to the residual interaction Ö Collectivity with thermal energy Ö Mass dependence Ö Configuration dependence Ö Measurement of Compound and Rotational Damping Width Ö Superdeformation at finite temperature i) how large the damping width Γ rot is and how it changes with excitation energy and spin; ii) at which energy rotational damping sets in and how gradual is the process; iii) whether or not this process depends on the intrinsic nuclear configuration, therefore leading to different effects in connection with different quantum numbers of the shell-model states, such as the K-quantum number; iv) how high in excitation energy one has to go before a fully chaotic regime is reached. A. Bracco and S. Leoni, Rep. Prog. Phys. 65(2002)299

6 N N (2) (2) path path N (2) path Ridge Valley I-2 I I Band Mixing Calculations 10 4 H = H - def ω J x + V res Valley N (2) path N (2) path 160 Importance 120 of Residual Interaction 120 N (2) path Ridge Evidence for Rotational Damping regular bands SDI SDI E γ (kev) Nilsson Cranking SDI inter E γ (kev) No Int No Int Ridge strongly SDI interacting bands Valley SDI I-2 I I E γ (kev) No Int No Int U 0 = 1 MeV Γ rot = 200 kev B. Herskind et al., PRL68(1992)3008

7 Sensitivity to Residual Interaction Type of Interaction and Interaction Strength N (2) path full SDI 168 Yb - Ridge L 2 P+QQ L 3 L 5 L 4 L E γ (kev) Type of Interaction Rotational Damping originates from high-multiple terms of two-body residual interaction M. Matsuo et al., NPA617,1 (1997) N (2) path /A 27.5/A 55/A Steps Interaction Strength < V 2 > SDI = 20 kev < V 2 > EXP = 14 kev Fig. 28 from discrete spectroscopy S. Leoni et al., Eur. Phys. J. A4, 229 (1999)

8 Collectivity with Thermal Energy Fractional Doppler Shift Analysis Yb γ-γ spectrum 0.8 E γ Backward <E γ >=800 kev (E γ1 -E γ2 ) kev F(τ) Q t =7.6 eb Q t =6.6 eb Q t =5.5 eb E2 BUMP VALLEY (Covariance) RIDGE DISCRETE E γ (kev) E γ Forward <E γ >=800 kev Backward Forward Same Collectivity Q t =5.5 eb B(E2) = 200 W.u (E γ1 -E γ2 ) kev E γ (kev) yrast discrete exc. bands mixed exc. bands S. Frattini et al., PRL81(1998)2659

9 Configuration Dependence & Onset of Chaos Persistence of selection Rules with Temperature: Chaotic regime: U 2.5 MeV Smaller number of High-K states in the damping regime Low K 10 High K Need for confirmation in other systems: egs. Hf nuclei 136 Te+ 48 Ca è 180 Hf +4n G. Benzoni et al.,plb (2005)

10 Warm rotation in exotic systems Stable: MeV)+ 124 Sn 168 Yb(63 )+4n SPES: MeV)+ 48 Ca 176 Yb(76 )+4n

11 Spin and temperature dependince of Γ rot Stable: MeV)+ 124 Sn 168 Yb(63 )+4n SPES: MeV)+ 48 Ca 176 Yb(76 )+4n Ca+ 124 Sn 132 Sn+ 48 Ca Γ rot I-2 I I+2 <U> [MeV] 4 2 γ-flow E1/E Spin [h] Γ rot [kev] I= Yb U [MeV] 40

12 Rotational Damping: I and T dependence Γ rot and Γ µ from γ-γ spectra E2 strength α> Er EUROBALL Data Γ rot Γ µ I-2 I-2 Δω 0 I fine structure of rotational damping Width [kev] <U> = 2 MeV <U> = 1.4 MeV Γ rot Γ rot 2Γ µ µ 150 I = 40, 41 h levels narrow Γ µ Γ 2 Counts [a.u.] Γ wide 50 2Γ rot Γ nar 50 discrete U < 1 MeV Spin [h] 0 Γ wide (E γ1 -E γ2 ) [kev] S. Leoni et al., PRL93(2004) F. Stephens et al., PRL88(2002) M. Matsuo et al., PLB465(1999)1

13 Shell effects dependence N (2) path N (2) path RIDGE ANALYSIS 168 Yb VALLEY ANALYSIS 164 Yb 114 Te theory 114 Te 164 Yb 114 Te theory E γ (kev) So far MASS dependence has been addressed Γ rot α I A -5/2 ε -1 U 0 α A -2/3 comparative study A=110 A= Te 164 Yb ε 0.25 ε 0.25 Γ rot depends on 2 contributions: P and N. Accessing nuclei on an isotopic chain wll help define the 2 contributions 168 Yb I=40h,U=2MeV highly aligned orbits no highly aligned orbits neutron for U 2 MeV Γ rot = 2(2Δω 0 ) Δω 0 = (Δω 0N ) 2 + (Δω 0P ) 2

14 Rotational Damping: I and T dependence

15 Proposed reactions

16 Experimental array Need for a 4π γ array: Ge Ball (AGATA/GALILEO) + LaBr 3 scintillators

17 Conclusions